produce spiking dynamics, I use a proper orthogonal decomposition (POD) to reduce
the number of state variables and a discrete empirical interpolation method (DEIM)
to reduce the complexity of the nonlinear terms.
The techniques described above are successful, but they inherently assume that the
whole neuron is either passive (linear) or active (nonlinear). However, in realistic cells
the voltage response at distal locations is nearly linear, while at proximal locations it
is very nonlinear. With this observation, I fuse the aforementioned models together
to create a reduced coupled model in which each reduction technique is used where
it is most advantageous, thereby making it possible to more accurately simulate a
larger class of cortical neurons.
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